𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On graphs whose line graphs have crossing number one

✍ Scribed by Stanislav Jendrol'; Marián Kles̆c̆


Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
118 KB
Volume
37
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis


Abstract

Necessary and sufficient conditions are given for a nonplanar graph to have a line graph with crossing number one. This corrects some errors in Kulli et al. 4. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 181–188, 2001


📜 SIMILAR VOLUMES


On Line Graphs with Crossing Number 1
✍ V. R. Kulli; D. G. Akka; L. W. Beineke 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 159 KB

## Abstract In this paper we deduce a necessary and sufficient condition for a line grah to have crossing number 1. In addition, we prove that the line graph of any nonplanar graph has crossing number greater than 2.

On 3-regular graphs having crossing numb
✍ Dan McQuillan; R. Bruce Richter 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 414 KB

## Abstract We give a planar proof of the fact that if __G__ is a 3‐regular graph minimal with respect to having crossing number at least 2, then the crossing number of __G__ is 2.

On graphs whose Laplacian matrices have
✍ Shaun M. Fallat; Stephen J. Kirkland; Jason J. Molitierno; M. Neumann 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 120 KB

## Abstract In this paper, we investigate graphs for which the corresponding Laplacian matrix has distinct integer eigenvalues. We define the set __S~i,n~__ to be the set of all integers from 0 to __n__, excluding __i__. If there exists a graph whose Laplacian matrix has this set as its eigenvalues

On graphs with subgraphs having large in
✍ Noga Alon; Benny Sudakov 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 131 KB

## Abstract Let __G__ be a graph on __n__ vertices in which every induced subgraph on ${s}={\log}^{3}\, {n}$ vertices has an independent set of size at least ${t}={\log}\, {n}$. What is the largest ${q}={q}{(n)}$ so that every such __G__ must contain an independent set of size at least __q__? This

On subpancyclic line graphs
✍ Xiong, Liming 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 160 KB 👁 1 views

We give a best possible Dirac-like condition for a graph G so that its line graph L(G) is subpancyclic, i.e., L(G) contains a cycle of length l for each l between 3 and the circumference of G. The result verifies the conjecture posed by Xiong (Pancyclic results in hamiltonian line graphs, in:

On hamiltonian line graphs
✍ Lane Clark 📂 Article 📅 1984 🏛 John Wiley and Sons 🌐 English ⚖ 191 KB